Free Fermions, vertex Hamiltonians, and lower-dimensional AdS/CFT

Abstract

In this paper we first demonstrate explicitly that the new models of integrable nearest-neighbour Hamiltonians recently introduced in PRL 125 (2020) 031604 satisfy the so-called free fermion condition. This both implies that all these models are amenable to reformulations as free fermion theories, and establishes the universality of this condition. We explicitly recast the transfer matrix in free fermion form for arbitrary number of sites in the 6-vertex sector, and on two sites in the 8-vertex sector, using a Bogoliubov transformation. We then put this observation to use in lower-dimensional instances of AdS/CFT integrable R-matrices, specifically pure Ramond-Ramond massless and massive AdS_3, mixed-flux relativistic AdS_3 and massless AdS_2. We also attack the class of models akin to AdS_5 with our free fermion machinery. In all cases we use the free fermion realisation to greatly simplify and reinterpret a wealth of known results, and to provide a very suggestive reformulation of the spectral problem in all these situations.

arXiv comment51 pages, no figures; v2: typos fixed and comments added; v3: 54 pages, typos and errors fixed, added comments, homogenised notation, added appendix

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• Integrable deformations of AdS/CFT
• Protected states in $\mbox{AdS}_3$ backgrounds from integrability
• Dynamical Spin Chains in 4D $\mathcal{N}=2$ SCFTs
• A study of integrable form factors in massless relativistic AdS_3
• Integrable models on Rydberg atom chains
• A study of integrable form factors in massless relativistic $Ad{S}_2$
• T-W relation and free energy of the antiperiodic XXZ chain with η=iπ/3 at a finite temperature
• Transfer matrices for AdS3/CFT2